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A novel embedded element pattern decomposition method is proposed to synthesize conformal phased antenna arrays. This method decomposes the embedded element patterns as a product of a characteristic matrix and a Vandermonde structured matrix. This Vandermonde matrix is composed of modes in the modal space at the sampling angles. Because the fast Fourier transform (FFT) algorithm can be used in the Vandermonde structure, the computational cost can be reduced tremendously. In addition to its computational efficiency, the proposed method is also applicable to the synthesis of a pattern with any mainlobe direction and optimized polarization. A modified particle swarm optimization (PSO) method is applied to optimize the weights of the modes. This method is demonstrated through a simulation of a 9-element conformal array. The results show the advantages of the new method in achieving a low peak side lobe, accurate mainlobe scanning, and low cross-polarization.